Merry Christmas

I wish all of my readers a merry Christmas! Things are going to be somewhat slow here on the blog for a few days, but I promise to be back in early January with more news about mathematics education research!

If you want to stay up to date, you might consider checking my shared articles on Google Reader, or you can go directly to the automatically updated articles within the field of mathematics education. Articles related to education research in general can be found here, and articles related to early childhood education can be found here. You might also consider following me on twitter, where I will also provide news and updates about mathematics education and other things of interest.


Teacher lust

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.

Learning to teach mathematics through inquiry

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.


TIMSS Advanced 2008

Last week, the results from the TIMSS Advanced 2008 were released. The TIMSS assessment is probably well known to most, and the TIMSS video studies might also be familiar to some, but what exactly is TIMSS Advanced? The following description from the official website might explain some of the confusion:
TIMSS Advanced 2008 assesses student achievement in advanced mathematics and physics in the final year of secondary school—the twelfth grade in many countries. TIMSS Advanced is part of IEA’s series of TIMSS international assessments designed to provide comparative information about educational achievement across countries. Because TIMSS Advanced assesses students in their last year of secondary school who have studied advanced mathematics or physics to prepare them for further study of mathematics and science at the tertiary level, the results are of particular importance for educational decision making. (Source: http://timss.bc.edu/timss_advanced/index.html)
If you want to take a closer look at the full report from this study, you can check out this link (this is a direct link to a 33MB pdf file!). In case you want to dig even deeper into all the details and documentation of this study, you might want to take a look at The TIMSS Advanced 2008 Technical Report (14MB).


Arora, A., Foy, P., Martin, M.O., & Mullis, I.V.S. (Eds.). (2009). TIMSS Advanced 2008 Technical Report. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.

Mullis, I.V.S., Martin, M.O., Robitaille, D.F., & Foy, P. (2009). TIMSS Advanced 2008 International Report: Findings from IEA's Study of Achievement in Advanced Mathematics and Physics in the Final Year of Secondary School. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.

Math tutoring for low-achieving students

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.


The increasing role of metacognitive skills in math

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.


Visual templates in pattern generalization activity

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.


Developing a 'leading identity'

Laura Black, Julian Williams, Paul Hernandez-Martinez, Pauline Davis, Maria Pampaka and geoff Wake have written an article called Developing a ‘leading identity’: the relationship between students’ mathematical identities and their career and higher education aspirations. This article was published online in Educational Studies in Mathematics last Wednesday. Here is the abstract of their article:
The construct of identity has been used widely in mathematics education in order to understand how students (and teachers) relate to and engage with the subject (Kaasila, 2007; Sfard & Prusak, 2005; Boaler, 2002). Drawing on cultural historical activity theory (CHAT), this paper adopts Leont’ev’s notion of leading activity in order to explore the key ‘significant’ activities that are implicated in the development of students’ reflexive understanding of self and how this may offer differing relations with mathematics. According to Leont’ev (1981), leading activities are those which are significant to the development of the individual’s psyche through the emergence of new motives for engagement. We suggest that alongside new motives for engagement comes a new understanding of self—a leading identity—which reflects a hierarchy of our motives. Narrative analysis of interviews with two students (aged 16–17 years old) in post-compulsory education, Mary and Lee, are presented. Mary holds a stable ‘vocational’ leading identity throughout her narrative and, thus, her motive for studying mathematics is defined by its ‘use value’ in terms of pursuing this vocation. In contrast, Lee develops a leading identity which is focused on the activity of studying and becoming a university student. As such, his motive for study is framed in terms of the exchange value of the qualifications he hopes to obtain. We argue that this empirical grounding of leading activity and leading identity offers new insights into students’ identity development.

"Me and maths"

Pietro Di Martino and Rosetta Zan have written an article entitled ‘Me and maths’: towards a definition of attitude grounded on students’ narratives. The article was published online in Journal of Mathematics Teacher Education on Friday. Here is a copy of the abstract of their article:
The attitude construct is widely used by teachers and researchers in mathematics education. Often, however, teachers’ diagnosis of ‘negative attitude’ is a causal attribution of students’ failure, perceived as global and uncontrollable, rather than an accurate interpretation of students’ behaviour, capable of steering future action. In order to make this diagnosis useful for dealing with students’ difficulties in mathematics, it is necessary to clarify the construct attitude from a theoretical viewpoint, while keeping in touch with the practice that motivates its use. With this aim, we investigated how students tell their own relationship with mathematics, proposing the essay “Me and maths” to more than 1,600 students (1st to 13th grade). A multidimensional characterisation of a student’s attitude towards mathematics emerges from this study. This characterisation and the study of the evolution of attitude have many important consequences for teachers’ practice and education. For example, the study shows how the relationship with mathematics is rarely told as stable, even by older students: this result suggests that it is never too late to change students’ attitude towards mathematics.