An investigation of preservice teachers’ use of guess and check in solving a semi open-ended mathematics problem

Open-ended problems have been regarded as powerful tools for teaching mathematics. This study examined the problem solving of eight mathematics/science middle-school teachers. A semi-structured interview was conducted with (PTs) after completing an open-ended triangle task with four unique solutions. Of particular emphasis was how the PTs used a specific heuristic strategy. The results showed that the primary strategy PTs employed in attempting to solve the triangle problem task was guess and check; however, from the PTs’ reflections, we found there existed misapplications of guess and check as a systematic problem-solving strategy. In order to prepare prospective teachers to effectively teach, teacher educators should pay more attention to the mathematical proficiency of PTs, particularly their abilities to systematically and efficiently use guess and check while solving problems and explain their solutions and reasoning to middle-school students.     

Addressing the role of working memory in mathematical word-problem solving when designing intervention for struggling learners

ZDM – Mathematics Education - The focus of this article is the well documented association between low working memory capacity and difficulty with mathematical word-problem solving. We begin...     

Unidirectional Littelmann Paths for Crystals of Type A and Rank 2

Algebras and Representation Theory - For the Kashiwara crystal of a highest weight representation of an affine Lie algebra of type A and rank e, with highest weight Λ, there is a labeling by...     

Connecting Mathematics and Science in Undergraduate Teacher Education Programs: Faculty Voices from the Maryland Collaborative for Teacher Preparation

The study reported in this paper investigated perceptions concerning connections between mathematics and science held by university/college instructors who participated in the Maryland Collaborative for Teacher Preparation (MCTP), an NSF-funded program aimed at developing special middle-level mathematics and science teachers. Specifically, we asked (a) “What are the perceptions of MCTP instructors about the ‘other’ discipline?” (b) “What are the perceptions of MCTP instructors about the connections between mathematics and science?” and (c) “What are some barriers perceived by MCTP instructors in implementing mathematics and science courses that emphasize connections?” The findings suggest that the benefits of emphasizing mathematics and science connections perceived by MCTP instructors were similar to the benefits reported by school teachers. The barriers reported were also similar. The participation in the project appeared to have encouraged MCTP instructors to grapple with some fundamental questions, like “What should be the nature of mathematics and science connections?” and “What is the nature of mathematics/science in relationship to the other discipline?”     

Kinetical Study of the Catalytic Hydrogenation of Catechol by Metals

In this paper, the kinetical study of catalytic hydrogenation of catechol over platinum metal catalysts in liquid phase under room temperature and one atmospheric pressure was investigated. Simple models “straight line” model 1 together with “triangle” model 2 were used to interpret for the change of compositions of samples traced during the reaction process, and the interpretation was found to be satisfactory. These models are as following: Model 1: consecutive reaction path catechol→2-hydroxycyclohexanone→cyclohexane-1,2-diol Model 2: catechol→cyclohexane-1, 2-diol directly was added to reaction path of model 1. The relative reaction rates during hydrogenation processes over ruthenium, rhodium, palladium and platinum were calculated too. It was also found that the strength of oxygen affinity with catalysts was the factor influenced the selectivity of reaction path and the stereoselectivity of cis and trans diol products.     

The structure of di-μ-pentafluorobenzoatobis[bis(pentafluorophenyl)(triphenylphosphine oxide)thallium(iii)]

An X-ray crystallographic study has shown that the complex (C₆H₅)₂TlO₂CC₆F₅(OPPh₃) has a dimeric structure with unsymmetrical pentafluorobenzoate bridging (TlO 2.531 and 2.789 Å) but an exact crystallographic centre of symmetry. The pentafluorobenzoate groups are also unsymmetrically chelated to thallium (TlO 2.389 and 2.531 Å.), which overall has irregular six coordination.     

Differentiation of teaching and learning mathematics: an action research study in tertiary education

Diversity and differentiation within our classrooms, at all levels of education, is nowadays a fact. It has been one of the biggest challenges for educators to respond to the needs of all students in such a mixed-ability classroom. Teachers’ inability to deal with students with different levels of readiness in a different way leads to school failure and all the negative outcomes that come with it. Differentiation of teaching and learning helps addressing this problem by respecting the different levels that exist in the classroom, and by responding to the needs of each learner. This article presents an action research study where a team of mathematics instructors and an expert in curriculum development developed and implemented a differentiated instruction learning environment in a first-year engineering calculus class at a university in Cyprus. This study provides evidence that differentiated instruction has a positive effect on student engagement and motivation and improves students’ understanding of difficult calculus concepts.     

Beliefs and Perspectives of First‐Year,Alternative Preparation,Elementary Teachers in Urban Classrooms

Results from an earlier study ( Hart, 2002 ) suggested that a group of 14 teachers participating in an alternative preparation program for elementary teachers had developed beliefs that were consistent with current thinking in mathematics education. The current study follows 8 of those teachers into their first year of teaching in an urban classroom. Qualitative data were collected from three sources: reflection logs, mathematics case discussions, and field notes made during classroom observations. This provided a triangulation of perspectives: the teachers' views of themselves, the teachers' views of others, and the university faculty member's view of them. Also, teachers completed the Standards Belief Instrument (Zollman & Mason, 1996) at the end of Phase I and at the end of Phase II. Results from the instrument and the qualitative analysis suggest that the teachers maintained a strong reform perspective in their beliefs, but they were unable to consistently implement pedagogy that was consistent with those beliefs.     

On the <Emphasis Type="Italic">KO</Emphasis> Characteristic Cycle of a Spin<Superscript><Emphasis Type="Italic">c</Emphasis></Superscript> Manifold

We compute the KO-characteristic numbers of a characteristic submanifold of a Spin^c manifold in terms of its K-characteristic numbers. The proof is based on the geometry of the Thom class in K-theory and is simpler than the existing proofs of several previously known special cases.