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.

F.D. Rivera has written an article called Visual templates in pattern generalization activity. The article was published online in Educational Studies in Mathematics last Thursday. The study, which is described in the article, was carried out in an eighth-grade Algebra 1 class in California. Four and a half months after a teaching experiment on pattern generalization, 11 students were interviewed (clinical interviews). Clinical interviews were also made with these students directly before and after the teaching experiment. The article reports on results from the analyses of these clinical interviews.

Here is the abstract of the article:

In this research article, I present evidence of the existence of visual templates in pattern generalization activity. Such templates initially emerged from a 3-week design-driven classroom teaching experiment on pattern generalization involving linear figural patterns and were assessed for existence in a clinical interview that was conducted four and a half months after the teaching experiment using three tasks (one ambiguous, two well defined). Drawing on the clinical interviews conducted with 11 seventh- and eighth-grade students, I discuss how their visual templates have spawned at least six types of algebraic generalizations. A visual template model is also presented that illustrates the distributed and a dynamically embedded nature of pattern generalization involving the following factors: pattern goodness effect; knowledge/action effects; and the triad of stage-driven grouping, structural unit, and analogy.

Roger G. Brown from the University of Leeds (UK) has written an article entitled Does the introduction of the graphics calculator into system-wide examinations lead to change in the types of mathematical skills tested? This article was published online in Educational Studies in Mathematics earlier this week. Here is the abstract of his article:

The paper reports on the introduction of the graphics calculator into three centralised examination systems, which were located in Denmark, Victoria (Australia) and the International Baccalaureate. The introduction of the graphics calculator required those responsible for writing examination questions to consider how to assess mathematical skills within this new environment. This paper illustrates the types of mathematics skills that have been assessed within the graphics-calculator-assumed environment. The analysis of the examination questions indicated that only two out of the six mathematics examinations considered demonstrated any significant change in the types of skills assessed in conjunction with the introduction of the graphics calculator. The results suggest that it is possible to reduce the use of questions assessing routine procedures (mechanical skills) with a graphics calculator, but it is also evident that there have not been major changes in the way that examination questions are written nor the mathematics skills which the questions are intended to assess.

Richard Lissaman, Sue de Pomerai and Sharon Tripconey have written an article that was recently published online in Teaching Mathematics and its Applications. The article is entitled Using live, online tutoring to inspire post 16 students to engage with higher level mathematics, and here is a copy of the article’s abstract:

In recent years, there has been a decline in the number of students aged 16–18 studying and being able to access higher level mathematics in schools in the UK. The Further Mathematics Network (FMN) was set up to enable access to such mathematics to all students and to promote and encourage students to study at this level. The FMN has pioneered the use of Elluminate, a well established web-based package, for live mathematics tutoring. Small groups of students meet online with an experienced tutor to learn new aspects of mathematics and to look at ways to solve complex problems. There are also extensive online resources to support the students’ learning. The findings are discussed in the following article.

The Nordic Journal of Research in Mathematics Education (NOMAD) has recently released the October issue. This issue contains three research articles:

• Leif Bjørn Skorpen: Nokre spesielle trekk ved arbeidet med matematikkfaget i begynnaropplæringa (in Norwegian)
• Frode Olav Haara and Kari Smith: Practical activities in mathematics teaching – mathematics teachers’ knowledge based reasons
• Diana Stentoft and Paola Valero:  Identities-in-action. Exploring the fragility of discourse and identity in learning mathematics