David Wagner and Brent Davis have written an article called Feeling number: grounding number sense in a sense of quantity. The article was published online in Educational Studies in Mathematics on Monday. In this interesting article, they draw upon different theories and ideas from psychology as well as cultural and linguistic studies. Here is the abstract of their article:¨

Drawing on results from psychology and from cultural and linguistic studies, we argue for an increased focus on developing quantity sense in school mathematics. We explore the notion of “feeling number”, a phrase that we offer in a twofold sense—resisting tendencies to feel numb-er (more numb) by developing a feeling for numbers and the quantities they represent. First, we distinguish between quantity sense and the relatively vague notion of number sense. Second, we consider the human capacity for quantity sense and place that in the context of related cultural issues, including verbal and symbolic representations of number. Third and more pragmatically, we offer teaching strategies that seem helpful in the development of quantity sense coupled with number sense. Finally, we argue that there is a moral imperative to connect number sense with such a quantity sense that allows students to feel the weight of numbers. It is important that learners develop a feeling for number, which includes a sense of what numbers are and what they can do.

In the present study we explore changes in perceptions of our class of prospective mathematics teachers (PTs) regarding their mathematical knowledge. The PTs engaged in problem posing activities in geometry, using the “What If Not?” (WIN) strategy, as part of their work on computerized inquiry-based activities. Data received from the PTs’ portfolios reveals that they believe that engaging in the inquiry-based activity enhanced both their mathematical and meta-mathematical knowledge. As to the mathematical knowledge, they deepened their knowledge regarding the geometrical concepts and shapes involved, and during the process of creating the problem and checking its validity and its solution, they deepened their understanding of the interconnections among the concepts and shapes involved. As to meta-mathematical knowledge, the PTs refer to aspects such as the meaning of the givens and their relations, validity of an argument, the importance and usefulness of the definitions of concepts and objects, and the importance of providing a formal proof.

Andrew M. Tyminski has written an article that was recently published online in Journal of Mathematics Teacher Education. The article is entitled Teacher lust: reconstructing the construct for mathematics instruction. Here is the abstract of Tyminski’s article:

Two collegiate mathematics courses for prospective elementary and middle grades teachers provide the context for the examination of Mary Boole’s construct of teacher lust. Through the use of classroom observations and instructor interviews, the author presents a refined conception of teacher lust. Two working aspects of the construct were identified: (1) enacted teacher lust; an observable action that may remove an opportunity for students to think about or engage in mathematics for themselves; and (2) experienced teacher lust; an internal impulse to act in the manner described. Empirical examples of each facet, differences between conscious and unconscious interactions with teacher lust, along with potential antecedents are discussed.

Jo Towers has written an article entitled Learning to teach mathematics through inquiry: a focus on the relationship between describing and enacting inquiry-oriented teaching. The article was published online in Journal of Mathematics Teacher Education last week. Here is the abstract of the article:

This article is based on one of the several case studies of recent graduates of a teacher education programme that is founded upon inquiry-based, field-oriented and learner-focussed principles and practices and that is centrally concerned with shaping teachers who can enact strong inquiry-based practices in Kindergarten to Grade 12 classrooms. The analysis draws on interviews with one graduate, and on video data collected in his multi-aged Grade 1/2 classroom, to explore some of the ways in which this new teacher enacted inquiry-based teaching approaches in his first year of teaching and to consider his capacity to communicate his understanding of inquiry. This article presents implications for beginning teachers’ collaborative practices, for the assessment of new teachers and for practices in preservice teacher education.

Ronnie Karsenty has written an article entitled Nonprofessional mathematics tutoring for low-achieving students in secondary schools: A case study. This article was published online in Educational Studies in Mathematics last week. The project that is reported in the article is part of a larger project (SHLAV – Hebrew acronym for Improving Mathematics Learning). The research questions in the study are:

1. Will nonprofessional tutoring be effective, in terms of improving students’ achievements in mathematics, and if so, to what extent?
2. Which factors will be identified by tutors as having the greatest impact on the success or failure of tutoring?

Here is the abstract of the article:

This article discusses the possibility of using nonprofessional tutoring as means for advancing low achievers in secondary school mathematics. In comparison with professional, paraprofessional, and peer tutoring, nonprofessional tutoring may seem less beneficial and, at first glance, inadequate. The described case study shows that nonprofessional tutors may contribute to students’ understanding and achievements, and thus, they can serve as an important assisting resource for mathematics teachers, especially in disadvantaged communities. In the study, young adults volunteered to tutor low-achieving students in an urban secondary school. Results showed a considerable mean gain in students’ grades. It is suggested that affective factors, as well as the instruction given to tutors by a specialized counselor, have played a major role in maintaining successful tutoring.

Manita Van der Stel, Marcel Veenman, Kim Deelen and Janine Haenen have written an article entitled The increasing role of metacognitive skills in math: a cross-sectional study from a developmental perspective. This article was published online in ZDM last week. The article is an Open Access article, so it is freely available for all to read, but here is a copy of the abstract to tickle your interest:

Both intelligence and metacognitive skillfulness have been regarded as important predictors of math performance. The role that metacognitive skills play in math, however, seems to be subjected to change over the early years of secondary education. Metacognitive skills seem to become more general (i.e., less domain-specific) by nature (Veenman and Spaans in Learn Individ Differ 15:159–176, 2005). Moreover, according to the monotonic development hypothesis (Alexander et al. in Dev Rev 15:1–37, 1995), metacognitive skills increase with age, independent of intellectual development. This hypothesis was tested in a study with 29 second-year students (13–14 years) and 30 third-year students (14–15 years) in secondary education. A standardized intelligence test was administered to all students. Participants solved math word problems with a difficulty level adapted to their age group. Thinking-aloud protocols were collected and analyzed on the frequency and quality of metacognitive activities. Another series of math word problems served as post-test. Results show that the frequency of metacognitive activity, especially those of planning and evaluation, increased with age. Intelligence was a strong predictor of math performance in 13- to 14-year-olds, but it was less prominent in 14- to 15-year-olds. Although the quality of metacognitive skills appeared to predict math performance in both age groups, its predictive power was stronger in 14- to 15-year-olds, even on top of intelligence. It bears relevance to math education, as it shows the increasing relevance of metacognitive skills to math learning with age.