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).

References
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.

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.

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.

Christopher Yakes and Jon R. Star have written an article that was recently published online in Journal of Mathematics Teacher Education. The article is entitled Using comparison to develop flexibility for teaching algebra. Here is the abstract of their article:

In this paper, we describe a one-day professional development activity for mathematics teachers that promoted the use of comparison as an instructional tool to develop students’ flexibility in algebra. Effective use of comparison in mathematics instruction involves using side-by-side presentation of problems and solution methods and subsequent student discussion of these multiple solution methods to highlight the similarities and differences among problem-solving techniques. The goals of the professional development activity were to make teachers aware of how to use comparison effectively in their instruction, as well as to impact teachers’ own flexibility in algebra by using comparison instructionally during the professional development. Our analysis of teachers’ experiences in the professional development activity suggests that when teachers were presented with techniques for effective use of comparison, their own understanding of multiple solution methods was reinforced. In addition, teachers began to question why they relied exclusively on one familiar method over others that are equally effective and perhaps more efficient and started to draw new connections between problem-solving methods. Finally, as a result of experiencing instructional use of comparison, teachers began to see value in teaching for flexibility and reported changing their own teaching practices.

International Journal of Studies in Mathematics Education is a new international peer-reviewed journal within the field of mathematics education. The editors of the journal are from Brazil, and the journal web-site is in both Portuguese and English. The journal also accepts submission of articles in Portuguese, English, French and Spanish. According to their own description of the journal:

The journal aims to stimulate reflection on mathematics education at all levels: to generate productive discussion; to encourage enquiry and research; to promote criticism and evaluation of ideas and procedures current in the field
It is intended for the mathematics educator who is aware that the learning and teaching of mathematics are complex enterprises about which much remains to be revealed and understood
It reflects both the variety of research concerns within the field and the range of methods used to study them. We accept for submission articles in Portuguese, English, French and Spanish. The journal emphasizes high-level articles that go beyond local or national interest.

The journal has an online submission system, and the Open Journal Systems is being used. The journal is an online journal, and it appears to have an Open Access philosophy, so that the articles will be freely available for everyone to read/download. The aims of the journal are:

• to stimulate reflection on mathematics education at all levels;
• to generate productive discussion;
• to encourage enquiry and research;
• to promote criticism and evaluation of ideas and procedures current in the field

Unfortunately, I cannot find an RSS feed yet, but I am definitely going to keep an eye on this journal even though!

The first issue of the journal is already available, and it contains several interesting articles. The following articles are in English:

• Gesture, conceptual integration and mathematical talk, by Laurie Edwards
• Learning in virtual environments: a methodology for the analysis of teacher discourse, by Marcello Bairral
• Teacher’s semiotic games in mathematics laboratory, by Ornella Robutti

On Thursday, we had a very nice seminar with Bharath Sriraman, or rather we had him as a visitor at University of Stavanger for the whole day! Bharath is professor of mathematical sciences at the University of Montana. He is also founder and editor of The Montana Mathematics Enthusiast, a great online journal within the field of mathematics education research, and editor of numerous other journals, book series, etc.

When he visited us on Thursday, he held a lecture with a focus on gifted students, one of his specialties. Here are my notes from the lecture:

Gifted students – presentation by Bharath Sriraman

How do we figure out if a student is gifted? Nature versus nurture – is it genetic, or is it due to upbringing. Why is it okay for a child to be talented in sports and not so much so in a subject like mathematics?

When it comes to funding, little money is spent on gifted education. (Less than 1% of the funding for special needs education – giftedness is viewed as a special need!)

In the U.S. there is an east versus west debate. Why are they doing so much better in the eastern systems? The western system is viewed as fostering creativity and freedom, but why is it that so many of the prodigies are from the eastern part of the world?

In the U.S., public schools are poorly funded, teachers are not held in high regard or paid well, etc.

Interesting fact:  U.S. has the highest prison population proportion in the western, developed world – 30% of the prisoners are high school dropouts.

In the Asian countries, there is a lot of focus on moral, hard work, perseverance, etc. Exams are very competitive! In the East, the point of an exam is to stratify the society. Late bloomers do not have a chance within the Eastern system! The U.S. (and Western) system, however, allows for a second chance.

As a teacher, there is always the potential conflict between equity and excellence! This could be seen as a false dichotomy! Alternative perspectives:

• The Hamilton tradition stressed elitism,
• whereas the Jacksonian tradition suggests that everyone is equal no matter what
• The Jeffersonian tradition stresses that you should give people equal opportunities, and then it is up to them to use these opportunities

Mathematical intelligence is considered as:

• a strong indicator of general intelligence
• numerical and spatial reasoning is part of the IQ score
• …

The construct of intelligence is controversial in many ways since the psychometric testing. History of IQ-test: Binet-Simon tests –> Stanford-Binet tests, etc. The modern Stanford-Binet test is very much like a mathematical test, and you don’t take into account socio-cultural and environmental variables. Still, it is very much used as a test for giftedness.

There are, however, some alternative views when it comes to discussing giftedness. Usiskin (Uni. Chicago) tried to classify the mathematical talent in the world in a hierarchy of Level 0 to Level 7.

• Level 0 – no talent. Adults who know very little mathematics
• Level 1 – culture level. Adults who have some number sense (comparable to grades 6-9), and they have learned it through usage
• Level 2 – represent the honors high school student
• Level 3 – the “terrific” student, those who score 750-800 on the SAT.
• Level 4 – the “exceptional” students, those who excel in math competitions
• Level 5 – represents the productive mathematician
• Level 6 – the exceptional mathematician
• Level 7 – the all-time greats, Fields medal winners in mathematics

There is a difference between Creativity and creativity (everyone has the latter, the former is related to being creative within a certain field).

There are lots of way to adapt the curriculum so that the gifted students get what they need.

Research shows that there are no harmful effect on early college admission – the students manage well, and they adapt well.

In the U.S. there is a lot of emphasis on the modeling-based curricula nowadays, and this gets a lot of funding. Several programs are made which are based on real-world situations. (one from Montana!)

After this interesting lecture, he gave a presentation of a new book that he has been editing together with Lyn English: Theories of Mathematics Education: Seeking new frontiers. The book is published by Springer, and has just been released. Bharath told that the book took him five years to finish, and it is definitely going to become an important contribution to our field!

Thanks a lot for the visit, Bharath, and for sharing this day with us! Hopefully, this is only going to be the first in a series of visits to Stavanger!

The 4th annual Maths Week Ireland takes place this week, and it is presented as an “all island celebration of mathematics” at the official website. The Irish Times published an interesting article about this yesterday. There are several activities going on during the week, and it is all “timed to coincide with the annual Hamilton Day” on October 16th. William Rowan Hamilton (1805-1865) was one of Ireland’s most famous mathematicians, and he was also a physicist and astronomer.

Make sure to check out the official website for a list of events!