Summer is here...

Summer is here, and it is vacation time. This year, I even plan on taking a break from the blog writing! If you want to stay up-to-date during the summer, you can always go here to read the RSS feed of some of my preferred journals. Otherwise, you will have to wait until August 10, which is when I'll be back at work.

I wish all of my readers a wonderful summer :-)


Flexible use of symbolic tools

Lisa B. Warner , Roberta Y. Schorr and Gary E. Davis have written an article called Flexible use of symbolic tools for problem solving, generalization, and explanation. The article was published online in ZDM last week. Here is the abstract of their article:

We provide evidence that student representations can serve different purposes in the context of classroom problem solving. A strategy used expressly to solve a problem might be represented in one way, and in another way when the problem is generalized or extended, and yet in another way when the solution strategy is explained to peers or a teacher. We discuss the apparent long-term memory implications this has regarding the preferences that students have for their original versus later developed representations, and how these preferences relate to the use of representational flexibility in classroom settings.


Iterating between lessons and concepts

Bethany Rittle-Johnson and Kenneth Koedinger have written an article entitled Iterating between lessons on concepts and procedures can improve mathematics knowledge. This article was published in the latest issue of British Journal of Educational Psychology. Here is the abstract of their article:


Knowledge of concepts and procedures seems to develop in an iterative fashion, with increases in one type of knowledge leading to increases in the other type of knowledge. This suggests that iterating between lessons on concepts and procedures may improve learning.

The purpose of the current study was to evaluate the instructional benefits of an iterative lesson sequence compared to a concepts-before-procedures sequence for students learning decimal place-value concepts and arithmetic procedures.

In two classroom experiments, sixth-grade students from two schools participated (N=77 and 26).

Students completed six decimal lessons on an intelligent-tutoring systems. In the iterative condition, lessons cycled between concept and procedure lessons. In the concepts-first condition, all concept lessons were presented before introducing the procedure lessons.

In both experiments, students in the iterative condition gained more knowledge of arithmetic procedures, including ability to transfer the procedures to problems with novel features. Knowledge of concepts was fairly comparable across conditions. Finally, pre-test knowledge of one type predicted gains in knowledge of the other type across experiments.

An iterative sequencing of lessons seems to facilitate learning and transfer, particularly of mathematical procedures. The findings support an iterative perspective for the development of knowledge of concepts and procedures.


Charting the microworld territory over time

Lulu Healy and Chronis Kynigos have written an article called Charting the microworld territory over time: design and construction in mathematics education. The article was published online in ZDM recently. Here is the abstract of their article:

The study discusses the development of theoretical ideas and constructs related to digital microworlds within the mathematics education community and their implications for interpretations of mathematics learning. Starting from Papert’s introduction of the concept during ICME 2 in 1972, we trace the evolution of theoretical approaches concerning the essence of the idea in an attempt to situate the notion of constructionism in the light of contemporary frameworks. We argue that microworlds, and the search for a learnable mathematics, have a continued relevance to mathematics education, but that the lens research attention has shifted over time, with the current foci on communal design, situated and embodied approaches and artefacts whose use crosses boundaries between different practices. To illustrate these shifts and the challenges that still remain, we present examples from our current work involving the use of microworlds for learning and teaching through communication, design and construction.