Working with math students at ALP involves a lot of exploration of numbers related to a student’s concrete understanding.  For example, if we’re comparing the size of a blue whale and a dolphin, a student may easily calculate the difference (90-12), but visualize the two animals as being very similar in size.  While the paper shows the correct answer, the student’s concrete understanding of the groups is limited.  To build this image, we might draw them to scale or go into the parking lot to measure the actual sizes to see that those 86 feet mean that many dolphins could swim alongside one blue whale.  This approach incorporates various manipulatives to connect real-world experiences to number concepts.

Florian Krause, a researcher at Raboud University in the Netherlands, is currently researching how the brain thinks about numbers.  He postulates that people either think spatially or non-spatially.  Those who think spatially see numbers on a continuum – a number line.  Those who think non-spatially see numbers in terms of the space taken up by the value or the weight of the value, for example.  He’s finding differences in brain structure among test subjects asked to respond to a math question.  MRI scans show that those who think spatially have more gray matter volume in an area of the brain associated with visual-spatial information.  Those who think more non-spatially about numbers have a greater gray matter volume in the area of the brain associated with semantic and conceptual processing.

Because traditional math instruction is based largely on the number line continuum approach, Krause theorizes that people who struggle with math would benefit from a different method of teaching that incorporates understanding numbers as they relate to their bodies and to their experience with the environment.

This research is exciting news to those of us who teach math both ways – spatially and non-spatially – because it confirms the importance of involving both areas of the brain in mathematical thinking.  I’m inclined to believe that most of us, no matter where our brains have the most gray matter volume, would benefit from a combination approach to math instruction – not just in the early grades, but throughout our academic careers.  Real-life scenarios involving math require an understanding from both realms, so it seems reasonable to expect our educational experience to encompass both.