Springer has published a new book with a focus on low achieving pupils in numeracy in a school context. The book is written by Brian Street, Dave Baker and Alison Tomlin, and it is entitled Navigating Numeracies. Here is a copy of the publisher’s description of the book:

The book aims to further understanding of why some pupils have low achievement in numeracy in the school context. The authors aim to achieve this by a relatively original view that focuses on numeracy as a social practice. They report on their investigations into the meanings and uses of numeracy in school and home and community contexts, using ethnographic-style approaches, including formal and informal interviews and observations. The book will be useful for policy, practice and further research into the teaching and learning of mathematics in schools. It will therefore be of interest to policy makers, teachers and practitioners, academics and practitioners in teacher education, education researchers, and parents and community leaders.

Thursday and Friday last week, we had the pleasure of arranging a seminar with Danish colleague Jeppe Skott here in Stavanger. The focus of the seminar was on research concerning teachers’ beliefs and their impact on their teaching of mathematics. About 20 people attended the seminar, and I enjoyed it very much!

Skott started off with a session on the historical background of research on beliefs in mathematics education research. He talked about the development of teacher training in the Scandinavian countries, and he pointed to some of the major international studies in recent years. Then he lead us back to the OEEC study from the early sixties, and in this connection, he introduced Bauersfeld’s three levels:

• Matter meant
• Matter taught
• Matter learnt

The problems of implementation were then brought up, and he referred to the ICMI Study of 1986 as an important source. This study claimed that:

Significant changes in school mathematics will only be achieved if there are marked changes in the perceptions and attitudes of these teachers and if they are assisted to develop necessary new skills.

A strong focus was thereby put on the teachers’ perceptions and attitudes. The focus on the teacher as the main problem in the implementation process was thereby presented, and much of the research did (and still do) refer to Ernest’s model of the relationship between the espoused and enacted beliefs of the mathematics teacher. A main issue here, according to Skott, is that the premise for this research is taken for granted, and it is not based on analysis of data!

As a further theoretical background for the discussion, he introduced theories concerning constructivism (radical and social) and other.

Skott then introduced us with some of his own research in this field, and he introduced the case of Christopher as an example. (See his 2001 article for more on this!) In relation to this example, Skott introduced some of his own concepts: school mathematics images (SMI) and critical incidents of practice (CIP).

On Friday, Skott brought up the difficult and interesting discussion about the nature and existence of beliefs, and how we investigate them. His initial claim was that “traditional beliefs research” had made it impossible to give a reasonable answer to the question about the
relationship between a teacher’s conceptions about a subject on the one hand, and the teaching practice on the other hand. The main reason for that is that the answer has already been given as a premise for the research: there is a strong relationship between the two. This has not
been based on empirical evidence, Skott claims.

He then introduced a discussion about methods in beliefs research, and he pointed to the study he and Tine Wedege made of the Nordic KappAbel contest as an example (PDF version of the report). In a discussion of data analysis, Skott introduced the constructivist version of grounded theory presented by Charmaz (2006) as an example.

In the final round, Skott made a strong emphasis on the importance of context in beliefs research, and the implications this has on choice of research methods, etc. Some of his main points were:

• Inconsistency between beliefs and practice is from the point of view of the observer
• Consistency is situated in practice
• It is NOT the teacher’s practice

This short summary does not cover all the interesting issues that Jeppe Skott brought up, but it is an attempt to point at some of the main issues that were discussed in a very interesting seminar. So, thanks a lot to Jeppe Skott for a great seminar, and welcome back to Stavanger 🙂

This is not something directly related to research in mathematics education, but it is surely related to mathematics education, and I find it so interesting that I wanted to post it anyway!

Dan Meyer is a high-school mathematics teacher from Santa Cruz, California. He recently decided to put his entire Geometry curriculum online. This includes every lesson plan, every handout, more than 2000 slides (in Keynote, Powerpoint and PDF) … everything from an entire year of geometry teaching! Everything is nicely ordered for the web, so that you can follow his plans from week 1 to week 38.

In my view, as a researcher and mathematics educator, this is an exemplary action! I know, there might be several teachers out there who are going to copy his ideas, and that is okay. On the other side, this provides a very nice insight into one teacher’s ideas and thinking, and being able to follow a course for an entire year like this is an excellent opportunity for a researcher as well. I only wish more teachers would follow up what Dan has done, because I think this provides an excellent example of how our “new” technologies can be used to improve our teaching profession!

I am still thinking about how I could make use of this as a researcher, and if you have ideas concerning this, please post a comment below!

There are a couple of interesting articles from regular news sites that have been published lately that you might be interested in reading. ABC News published an article about math tests for kindergartners on August 28, and this article raises several important issues. The article is entitled NYC Schools Eye Math Tests for Kindergartners. The issue is that “New York City is asking public school principals to consider giving math tests to kindergartners, a proposal that comes amid debate over the growing use of standardized tests nationwide.”

The other article was published in Washington Post on Monday, and it aims at giving an overview of issues related to mathematics education. Some of the main issues in the article are:

• How is math taught?
• How much math is taught?
• What’s the fuss over math?
• When should kids learn algebra?

At the end of the article, they give a sample of some mathematics textbooks that are used in school (in the US). The article is, of course, very much headed towards issues in the US, but I find it interesting even though.

A couple of research reports have recently been published on the IES (Institute of Education Sciences) web page that might be of interest to some:

• Math education practices for students with disabilities and other struggling learners: case studies of six schools in two Northeast and Islands Region states
• Performance patterns for students with disabilities in grade 4 mathematics education in Massachusetts

Mathematics in school is a major issue in the US. Yesterday, Washington Post printed an article about a review of the mathematics curriculum in Loudoun County (Virginia). This county has introduced a curriculum for elementary school that is called Math Investigations, and there appears to be lots of critics who claim the curriculum fails to teach basic math skills. So, in the eyes of someone from outside the US context, this appears to be related to the so-called Math Wars. I am not trying to make any judgments in this debate, but it is interesting to be a spectator!

After reading about the curriculum on the web, I find it quite interesting. The curriculum was developed in the 1990s, and it was developed with support from the National Science Foundation. From their website, I learn that the Investigations in Number, Data, and Space (which is the official name of the curriculum, it appears) was designed to:

• Support students to make sense of mathematics and learn that they can be mathematical thinkers.
• Focus on computational fluency with whole numbers as a major goal of the elementary grades.
• Provide substantive work in important areas of mathematics—rational numbers, geometry, measurement, data, and early algebra—and connections among them.
• Emphasize reasoning about mathematical ideas.
• Communicate mathematics content and pedagogy to teachers.
• Engage the range of learners in understanding mathematics.

The guiding principles underlying these goals are that students have mathematical ideas, (…) teachers are engaged in ongoing learning about mathematics content, pedagogy, and student learning (…) and that teachers collaborate with the students and curriculum materials to create the curriculum as enacted in the classroom (quoted from their website). In many ways, the Investigations curriculum appears to have some common underlying ideas with the Everyday Math curriculum (which has also been strongly criticized by some). According to several impact studies, the Investigations curriculum appears to have a positive impact on the achievement of students, and Everyday Math is also a curriculum that is strongly based on research. As someone standing outside of this debackle, I am therefore somewhat amazed by the criticism these curricula has raised. Somewhat, but maybe not all that amazed after all. Our previous Norwegian curriculum (called L97) featured some of the same ideas about teaching and learning of mathematics, with a focus on letting the students discover and reinvent the mathematical ideas, having “mathematics in everyday life” as a main area of the curriculum, etc. After less than 10 years of implementations (evaluation reports showing that the curriculum had not really been implemented in the classrooms), it was replaced by a new curriculum called “Kunnskapsløftet” (Knowledge Promotion). This curriculum has a much stronger emphasis on basic skills, little or no mention of discovery and reinvention, little emphasis on connections with everyday life, etc. So, I guess this debate is not only typical for the US and in this case Loudoun county.

For me as a researcher, I think it is interesting to see how much resistance these “reform curriculum” efforts encounter, and it reminds me of something I read in The teaching gap. Teaching of mathematics appears to be some kind of cultural entity, and I think Stigler and Hiebert used the notion: “cultural scripts”. In order to implement a new curriculum, it is often necessary to change some of these cultural scripts, and that appears to be a rather cumbersome endeavor…

P.S. If any of you has some references to research, articles, etc. that relates to the above mentioned curriculum papers, please let me know!

This article was written by Paul Lockhart and published by MAA. I quote part of their introduction to the article:

This month’s column is devoted to an article called A Mathematician’s Lament, written by Paul Lockhart in 2002. Paul is a mathematics teacher at Saint Ann’s School in Brooklyn, New York. His article has been circulating through parts of the mathematics and math ed communities ever since, but he never published it. I came across it by accident a few months ago, and decided at once I wanted to give it wider exposure. I contacted Paul, and he agreed to have me publish his “lament” on MAA Online. It is, quite frankly, one of the best critiques of current K-12 mathematics education I have ever seen. Written by a first-class research mathematician who elected to devote his teaching career to K-!2 education.

The Montana Mathematics Enthusiast and editor Bharath Sriraman has released a new monograph. This time it is about Creativity, Giftedness, and Talent Development in Mathematics. Here is a copy of the web presentation of the monograph:

Our innovative spirit and creativity lies beneath the comforts and security of today’s technologically evolved society. Scientists, inventors, investors, artists and leaders play a vital role in the advancement and transmission of knowledge. Mathematics, in particular, plays a central role in numerous professions and has historically served as the gatekeeper to numerous other areas of study, particularly the hard sciences, engineering and business. Mathematics is also a major component in standardized tests in the U.S., and in university entrance exams in numerous parts of world.

Creativity and imagination is often evident when young children begin to develop numeric and spatial concepts, and explore mathematical tasks that capture their interest. Creativity is also an essential ingredient in the work of professional mathematicians. Yet, the bulk of mathematical thinking encouraged in the institutionalized setting of schools is focused on rote learning, memorization, and the mastery of numerous skills to solve specific problems prescribed by the curricula or aimed at standardized testing. Given the lack of research based perspectives on talent development in mathematics education, this monograph is specifically focused on contributions towards the constructs of creativity and giftedness in mathematics. This monograph presents new perspectives for talent development in the mathematics classroom and gives insights into the psychology of creativity and giftedness. The book is aimed at classroom teachers, coordinators of gifted programs, math contest coaches, graduate students and researchers interested in creativity, giftedness, and talent development in mathematics.

In Norway, we are now in the middle of our summer holidays, and I too have some lazy days with my family. Because of this, I don’t have the opportunity to keep this blog as frequently updated as I normally do. If you want to keep more up to date the last week of my holidays, you should check out this automatically updated site of all the journals I follow!