Observations from a First Timer at ICME-10
As a first time participant at the International Congress of Math Educators (ICME) I was fascinated on a number of fronts. ICME is held every four years at different locations throughout the world. This year's meeting (ICME-10) was hosted by a Scandinavian consortium in Copenhagen, Denmark. The conference ran from Sunday July 3 to Sunday July 11. I went as part of a five-member team from our LSC project, Valle Imperial Mathematics, to do a workshop presentation concerning how to make math word problems more accessible to English Language Learners.
The observations expressed here are, of course, my own and thus are limited in scope, but I wanted to share some of my learning in hope that others might gain some insight and/or validation of their efforts in math education. I know it might sound cliche-ish, but being able to talk to people from all over the world about their math programs was just awesome. I was really interested in learning first hand what was happening in mathematics in places with noted high math achievement such as Japan, Korea, and Singapore. I was also curious about what was happening in Russia now days, and since this was a Nordic hosted event, mathematics education in Finland came prominently into view.
The conference was set up to begin each day with a lecture from a math researcher. Then the rest of day was composed of various special interest topic and discussion group sessions. Many participants had set up poster displays of their research and sessions were conducted to discuss the posters. Time was also afforded in the afternoons for workshops. Participants were not left wanting for choice of activities.
Here are some of the "ah ha's" I gleaned along the way:
Math educators are concerned about math achievement in all of their countries. No duh! What I found curious was that even in Japan and Singapore that have traditionally done well on world testing such as TIMSS, math teachers, according to the researchers, don't think their students are achieving. I was somewhat surprised to learn that dependence on more traditional procedures that have produced good results on standardized tests are under growing scrutiny because it was felt by teachers that students didn't have enough flexibility and creativity in problem solving. However, a strong emphasis in the facilitation of composing and decomposing numbers was still vital, especially as a foundational skill in lower grades. E.g. 6 + 8 = (4 + 2) + 8 = 4 + (2 + 8) = 4 + 10 = 14. Composition and decomposition of numbers leads to better number sense, which is many times lost in our rush in the US to memorize number facts.
Multiple representations of problem solutions are becoming prominate in helping students reflect a more in depth understanding of the problems they are solving. I attended a presentation by Khoon Yoong Wong from Singapore in which he shared a model he uses with students which requires them to present a solution in six different ways: number, symbol, words, story, diagram, and "real thing" (use of a manipulative or model).
Pekka Kupari, a researcher from Finland, in his study: "Recent Developments in Finnish Mathematics Education," notes that there is no one factor that is at the fore in high math achievement in Finland. Content for teachers is important, but having good pedagogy is important as well. One factor that he did highlight in his lecture he found particularly noteworthy was that for high achieving 7th graders, math "self esteem" played a significant role. The more students saw themselves as having good problem solving abilities, the better they could solve problems. This again, is not surprising, but it does point to the fact that teachers, especially in elementary grades, need to be very cognizant of the self-image their students are formulating in mathematics. Reliance on rules and procedures may help some, but helping students have success at problem solving produces the greater self-esteem for more students. If we want children to be problems solvers, we must give them problems to solve and not shy away from the dreaded word problems. Our own research here in working with Cognitively Guided Instruction (CGI) bears this out. Children have a much different attitude toward mathematics and problem solving when they have multiple ways to solve problems. This goes a long way toward fostering the self-esteem vital for upper grade achievement. Kupari did also go on to say that he felt more research needed to be done concerning the affect teacher/student interaction has on math achievement. When I asked what this research should entail; he only repeated that it needed to be done.
This was one aspect of the conference that I found disappointing. Since the majority of participants were composed of researchers and college educators, there was research in abundance. However, most of the research pointed to problems without offering suggestions for solutions. Many studies pointed out that this or that needed to be done, but didn't offer any ideas for making perceived changes. For teachers and staff developers like us, mining in this area for new innovations proved to be a pretty fruitless task.
Still, the poster displays did provide numerous opportunities to see applications of research and glean ideas. For example, Susan Beal and Jamie Grow-Maienza from the US have been working with translating Korean elementary math curriculum into English and trying it with US students. When compared with students using curriculums from the US, the students using the Korean curriculum had higher achievement. A poster by Elsa Medina, mathematics education professor at Cal. Poly. San Luis Obispo, observed in working with future elementary teachers: "Many students perceive mathematics as something to be memorized rather than to be investigated. This perception tends to create animosity from students toward any problem from which they do not have an immediate solution or problems which require considerations of multiple cases." This attitude is most often later passed on when the teacher acquires a class of his or her own, and the cycle of misunderstanding, inaccessibility, and displeasure with mathematics is perpetuated.
In one of my special interest sessions the presenter was having us do an activity using a number chart in calling out compliments of numbers. She would have us answer at times in English and at times in one's first language. These times presented a cacophony of sounds, after which she observed how interesting it was to hear all of the languages. Then she poignantly stated, "If you are teaching young children, you have many languaged classroom in your own language." This is a point I believe all teachers should ponder.
As I previously stated, all in all, the conference was a very worthwhile learning experience. The research presentations gave us much to think about in terms of coming up with strategies to address the myriad of problems promulgated, as well as validating that many of our own beliefs and practices are on the right course to help improve mathematics achievement here in the US. Discussion groups provided opportunities to discuss math issues face to face with math educators from around the world. The international networking connections we have thus established will prove to be of great value to our future work with teachers here in the US as we now have additional resources interested in dialoguing with us and offering advice as we endeavor to make mathematics more accessible to teachers and students.
The next meeting of ICME will be held in Mexico in 2008. I would definitely recommend going.